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Theorem txprel 30646
Description: A tail Cartesian product is a relationship. (Contributed by Scott Fenton, 31-Mar-2012.)
Assertion
Ref Expression
txprel  |-  Rel  ( A  (x)  B )

Proof of Theorem txprel
StepHypRef Expression
1 txpss3v 30645 . . 3  |-  ( A 
(x)  B )  C_  ( _V  X.  ( _V  X.  _V ) )
2 xpss 4941 . . 3  |-  ( _V 
X.  ( _V  X.  _V ) )  C_  ( _V  X.  _V )
31, 2sstri 3441 . 2  |-  ( A 
(x)  B )  C_  ( _V  X.  _V )
4 df-rel 4841 . 2  |-  ( Rel  ( A  (x)  B
)  <->  ( A  (x)  B )  C_  ( _V  X.  _V ) )
53, 4mpbir 213 1  |-  Rel  ( A  (x)  B )
Colors of variables: wff setvar class
Syntax hints:   _Vcvv 3045    C_ wss 3404    X. cxp 4832   Rel wrel 4839    (x) ctxp 30596
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-9 1896  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431  ax-sep 4525  ax-nul 4534  ax-pr 4639
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 987  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-eu 2303  df-mo 2304  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ne 2624  df-ral 2742  df-rex 2743  df-rab 2746  df-v 3047  df-dif 3407  df-un 3409  df-in 3411  df-ss 3418  df-nul 3732  df-if 3882  df-sn 3969  df-pr 3971  df-op 3975  df-br 4403  df-opab 4462  df-xp 4840  df-rel 4841  df-cnv 4842  df-co 4843  df-res 4846  df-txp 30620
This theorem is referenced by:  pprodss4v  30651
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